maths hw(因式分解)

1) f(x)=x^3 -2x^2 - 9x + 18
= (x^2)(x-2) - 9(x - 2)
= (x^2 - 9)(x-2)
= (x-2)^2 (x+2)

2) x^2 - (y-z)^2
= [ x-(y-z) ] [x + (y-z) ]
= (x-y+z)(x+y-z)

3) a^2 - ab + 2a -2b
= (a)(a-b) + (2)(a-b)
= (a+2)(a-b)

4) 169y^2 - 25
= (13y)^2 - 5^2
= (13y-5)(13y+5)

5) 4x^2 - 4xy + y^2
= (2x-y)(2x-y)
= (2x-y)^2

6) 2x^2 - 4xy + y^2 - 2x + y
= (2x-y)^2 - 2x + y
= (2x-y)^2 - (2x-y)
= (2x-y) (2x-y-1)

7) 3b-ab = b(3-a)
8) 9-a^2 = 3^2 - a^2
= (3-a)(3+a)

9) 9-a^2 + 3b-ab
= (3-a)(3+a) + (b)(3-a)
= (3-a) [(3+a) + b]
= (3-a) (3+a+b)

Hope can help =]

1) f(x)=x^3 -2x^2 - 9x + 18


= (x^2)(x-2)-9(x - 2)---------------因式分解


= (x^2-9)(x-2)-----------------------抽x-2


= (x-2)^2(x+2)-----------------------答案


驗算：


(x-2)^2(x+2)


＝(x-2)^2(x+2)


= (x^2-9)(x-2)


=(x^2)(x-2)-9(x - 2)


=x^3 -2x^2 - 9x + 18


so, the answer is right.


2) x^2 - (y-z)^2


= [x-(y-z)][x+(y-z)]


= (x-y+z)(x+y-z)----------抽-x-y+z　　　
　

驗算:

(x-y+z)(x+y-z)


= [x-(y-z)][x+(y-z)]


=x^2 - (y-z)^2


so, the answer is right.


3) a^2 - ab + 2a -2b


= (a)(a-b) + (2)(a-b)--------因式分解


= (a+2)(a-b)


check:


(a+2)(a-b)


=(a)(a-b) + (2)(a-b)


=a^2 - ab + 2a -2b


so,the answer is right.


4) 169y² - 25


= (13y)² - 5²-------------a²b²=(ab)²


= (13y-5)(13y+5)-----------a²-b²=(a+b)(a-b)


check:


(13y-5)(13y+5)


=(13y)² - 5²


=169y² - 25


so,the answer is right.


5) 4x^2 - 4xy + y^2



= (2x-y)(2x-y)----------十字相乘法


= (2x-y)^2


十字相乘法:


2x↘-y

2x↗-y
----------

-2xy-2xy=-4xy


so,the answer is right.


6) 2x² - 4xy + y² - 2x + y


= (2x-y)²-2x+y--------------十字相乘法


十字相乘法:

2x↘-y
2x↗-y
------------
-2xy-2xy=-4xy



= (2x-y)^2 - (2x-y)


= (2x-y) (2x-y-1)----------抽2x-y


7) 3b-ab


= b(3-a)---------------------抽b


8) 9-a²


= 3² - a²


= (3-a)(3+a)--------a²-b²=(a+b)(a-b)/(a-b)(a+b)



9) 9-a² + 3b-ab


= (3-a)(3+a) + (b)(3-a)-------a²-b²=(a+b)(a-b)/(a-b)(a+b),抽b


= (3-a) [(3+a) + b]-----------抽3-a


= (3-a) (3+a+b)

2007-11-09 12:11:02 補充：
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